Computing economic power distribution in power tools

ABSTRACT

The economic dispatch of generation in interconnected areas is computed by determining the generation which will cause the incremental cost of power at each of the interarea tie points, as calculated from the interconnected areas, to be equal at the existing load level. A computer having its own loss matrix is utilized in each area. It computes the tie point costs on the basis of cost information sent from the areas interconnected to it, and it also sends its own costs to those areas. In each area the desired generation and net tie line interchange are computed to provide a basis for controlling the area&#39;&#39;s generation.

United States Patent Stadlin et al.

[54] COMPUTING ECONOMIC POWER DISTRIBUTION IN POWER TOOLS [72]Inventors: Walter O. Stadlin, Eagleville; Bruce F. Wollenberg, Chalfont,both of Pa.

[73] Assignee: Leeds & Northrup Company,

Philadelphia, Pa.

221 Filed: Sept. 8, 1970 [21] Appl. No.: 70,274

[52] U.S.Cl. ..235/l51.2l,444ll, 307/57 [51] Int. Cl ..G06l 15/56, 006i"l5/O6, H02) 3/06 [58] Field of Search ..235/l5l.2l, 150; 307/57;

[561 References Cited UNITED STATES PATENTS 3,400,258 9/1968 Stadlin..235/l5 l .21

Primary ExaminerEugene 0. Bot:

Assistant Examiner-Edward 1. Wise Attorney-William G. Miller, Jr. andRaymond F. MacKay [57] ABSTRACT The economic dispatch of generation inintercon nected areas is computed by determining the generation whichwill cause the incremental cost of power at each of the interarea tiepoints, as calculated from the interconnected areas. to be equal at theexisting load level. A computer having its own loss matrix is utilizedin each area. It computes the tie point costs on the basis of costinformation sent from the areas interconnected to it, and it also sendsits own costs to those areas. In each area the desired generation andnet tie line interchange are computed to provide a basis for controllingthe area's generation.

6 Claims, 5 Drawing Figures PATENEBAUG 8 1972 SHEET 1 BF 5 FIG. 1

INVENTORS' WALTER 0. STADLIN BRUCE F. WOLLENBERG tum-a... Arfiwzm AGENTPATENTED M1 8 I972 SHEET 2 BF 5 AREA EDC l DO N TIMES TO CONVERGE FIG. 2

DO FOR E ACH LOSS MATRIX INPUT DO M TIMES l 2P =EP =0 A ed A id 4 00 FOREACH SOURCE OF POWER GENERATOR TIE UNE 2P =2P +P A qd A gd gd STORE PAND EP STORE u HSPm PM Pt ,P| 1 OR PH f rd m+ ra 29. bPg 1 PM AND SP"CONTNUE AX 'QSAX CONTlNUE 'ERROR sxwb/ com-mus PATENTEDAUB 819723.683.161

sum 5 0r 5 AREA EDC 52 no N mass TO convenes 84 CONTINUE as 9e P P YCONTINUE cou1'muz v N u ERROR EXIT To HM COMPUTING ECONOMIC POWERDISTRIBUTION IN POWER TOOLS BACKGROUND OF THE INVENTION This inventionrelates to a method for the computation of the allocation of generationas between a plurality of generators interconnected in groups to formseparate areas with the areas in turn being intercom nected by tie linesto form a power pool. More particularly, this invention relates to amethod for computing the generation required of each of the generatorsmaking up the separate areas to establish for the power pool a minimumtotal cost for the power generated by the pool for the purpose ofobtaining maximum economy of operation while meeting the loadrequirements of the pool and its scheduled interchange with other pools.

In the past, the computation of the allocation of generation among theseparate generators of the interconnected areas of a pool has involvedthe use of computers which utilize a loss matrix or similar method forintroducing into the computations the effect of transmission losses. Theparameters of the matrix related to the overall computation probleminvolved in the pool as contrasted with a loss matrix which utilizesparameters which related only to the particular losses involved in theindividual areas of the pool. Thus, in earlier systems such as thesystem shown in U.S. Pat. No. 3,400,258, issued to one of the presentinventors on Sept. 3, 1968, means have been described for thecalculation of the desired generation for each of the generatingstations of the separate areas of the pools but by virtue of theincorporation of the constants relating to the transmission losses ofthe pool in a single matrix in addition to the incorporation of the lossconstant dealing with a particular area in still another matrix therehas been a duplication of computational facilities in order to makepossible the separate and individual operation of the areas in the poolwith predetermined tie line flows between them as compared with theoperation of the pool with an economic distribution of the totalgeneration so that the tie line flows between the areas carried out theeconomic distribution desired.

In some systems for computing the generation at the various generatingstations of each area as well as the power interchange between theareas, it has been necessary to utilize means for dealing with aplurality of interconnecting tie lines between some of the individualareas by calculating an average condition for those tie lines as, forexample, in the system described in Economic Control of InterconnectedSystems" by Leon K. Kirchmayer, published by John Wiley & Sons, I959.

Still other systems for calculating the values of generation and theinterchange power between the areas have been disclosed, for example, inthe Kirchmayer US. Pat. No. 3,117,221, issued Jan. 7, 1964, whereinthere has been incorporated a computation not only of the transmissionlosses but also of the cost of wheeling power through an area.

It is, therefore, an object of this invention to provide a novel methodfor determining the desired generation for the generators in theseparate areas interconnected to form a power pool so as to constantlymaintain maximum economy of operation for the pool consistant withrestrictions on generator and tie line loading.

A further object of this invention is the provision of a novel methodfor determining the desired generation for the generators of thestations in the separate interconnected areas of the pool as requiredfor maximum economy of operation of the pool while taking into accountthe transmission losses on the tie lines interconnecting the areas.

A still further object of this invention is the provision of a novelmethod for establishing signals representing the desired generation forthe generators making up the pool as may be required for satisfying theload of the pool while taking into account the transmission losses ontie lines between the areas with the use of a separate computer for eachof the areas.

Still another object of this invention is the provision of a means forcomputing the economic distribution of total generation in a power poolfor maximum economy without the utilization of a pool loss matrix or itsequivalent.

SUMMARY OF THE INVENTION In carrying out the present invention there isprovided a method for automatically computing the economic distributionof the generation in a group of areas interconnected for thetransmission of power therebetween when at least two of these areas areinterconnected by a plurality of transmission lines. This methodcomprises several steps of which the first is the automatic computationof the incremental cost of power at a boundary point on each tie linebetween that area and the areas interconnected thereto, based on theincremental generation costs and the incremental transmission losses inthat area. The method also includes the step of automatically computingin each of the areas interconnected thereto a second incremental cost ofpower at the same boundary points mentioned above based on theincremental cost of power generation and the incremental cost oftransmission losses in the interconnected areas. In addition, there isincluded the step of automatically comparing for each area, the firstand second incremental costs calculated for each of the boundary pointsas set forth above and then as a final step there is an automaticcomputation from the results of this comparison, of the magnitude of thepower generation required from each of the power sources and the netinterarea tie line interchanges on each of the ties between therespective areas as needed to maintain equality between the sum of thetotal actual generation and the total actual interchange of the area andthe sum of the desired generation and the desired tie line interchangesas computed.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a diagrammatic showing of apower pool showing the tie lines between the individual areas and thecommunications channels needed between the computers of the areas.

FIGS. 2, 3, 4 and 5 are block diagrams of parts of the algorithm to befollowed by a digital computer in making the necessary calculations.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows a power pool 10which includes 4 interconnected areas, namely areas I, 2, 3 and 4. AreaI is shown as having transmission lines 12 and 13 connecting it to area2 for the interchange of power therebetween. Area 1 is also connected bytransmission lines 14 and 15 to areas 4 and 3, respectively. There isalso shown a plurality of tie lines 16 and 17 connecting area 4 and area3 for interchange of power between those areas while the tie line 18connects area 3 to area 2. Areas 1, 2 and 4 have tie lines 20, 21, 22and 23 which connect to other power pools. For example. tie lines 20 and21 connect area 1 to an external power pool and the tie lines 22 and 23connect areas 2 and 4 respectively to other pools.

As shown in FIG. 1, each of the areas may incorporate a number ofgeneration sources such as the generator 24 whose actual output P issupplied to a station or generator bus 26 at which point the incrementalcost of generating power C may be determined as will be explainedsubsequently. The power generated in each of the areas is absorbed bythe loads of the areas (not shown) and is also transmitted as requiredover the individual tie lines interconnecting each individual area toother areas of the pool.

Each of the areas of the power pool is shown as having a computer suchas the computer 31 of area 1 whose purpose is to compute the desiredgeneration, P for each of the generators in the area as well as thedesired net tie line interchange 2 for that area. This computation ineach of the computers 31-34 is preferably made by a digital computer inaccordance with a program following the algorithm to be describedsubsequently. This computation requires that each of the computers haveas an input the measured value of the actual generation for each of thegenerators in the particular area P as well as a measured value for theactual tie line flow over the tie lines into the particular area P Inaddition to these measured values, which are made in the particular areain which the computer is located (the local area), the computer of eacharea must receive from the computer of each area to which it isinterconnected (the foreign areas) the following information based uponvalues computed during the last economic dispatch computation made bythe computers of the foreign areas:

P,],= the tie line power flow over each tie line to the local area froma foreign area.

C,],= the incremental cost at a tie point on each tie line associatedwith the flow of the power P,],. g :]r=IhG rate of change of theincremental cost of power flow over each tie line with changes in tieline power flow evaluated in the region of Pd,

In addition it will be necessary to introduce into the computers 31-34measured values of the sum of the tie line interchanges between theparticular area and the interconnected areas of the pool 2P which forarea 1 in pool 10 of FIG. 1 is the sumriiation of the tie line flowsover the ties 12-15. Also, it is necessary to sum up the tie line flowsto other pools as, for example, by measuring P which in FIG. 1 is shownas including the measurement of the tie line power flow over the ties20-23.

As will be described subsequently, it will be necessary to calculate theincremental cost C, of power at the tie points on the interarea tiessuch as shown on tie line 12. The points at which these costs may becalculated can be at a particular bus to which the tie is connected orat other points, wherever it is convenient for purposes of power systemoperation.

It will be noted that each of the computers 31-34 has communicationchannels shown by dashed lines interconnecting the computers in theareas which are interconnected by tie lines. Over the communicationchannels 41, 42 and 43 the necessary information is sent from therespective computers 32, 33 and 34 to computer 31 while over thechannels 41 and 42 similar information is sent back from computer 31 tocomputers 32 and 33. The communications over channel 43 suppliesinformation between computer 34 and computer 31. Computer 34 is in thereference area, namely area 4. Communications channels 46 and 47,respectively, connect the computers 34 and 33 in one case and 33 and 32in the other case with communications over both channels going in bothdirections. Thus, as will be evident from FIG. 1, it will be necessaryto have communication channels between all areas which haveinterconnecting tie lines between them for the purpose of interchangingthe information described above.

Fundamental economic theory has demonstrated that the incremental cost(dollars/MWh) at any point on a power system must be the same whencomputed from all connecting areas for the system to be in economicbalance. This principle has been applied to generators within an areaas, for example, in U.S. Pat. No. 2,836,730 issued to E. D. Early on May27, 1958 and U.S. Pat. No. 2,836,731 issued to W. G. Miller, Jr. on May27, I958. Likewise, the principle can be applied to the interchangeamong areas as illustrated in U.S. Pat. No. 3,l l7,22l issued to L. K.Kirchmayer on Jan. 7, 1964 and also illustrated in U.S. Pat. No.3,400,258 issued to W. O. Stadlin, one of the present inventors, onSept. 3, [968. Further theoretical background for this proposition maybe found in the previously mentioned publication Economic Control ofInterconnected Systems," by Leon K. Kirchmayer.

For control of power interchange between areas of an interconnection tobe advantageous to the areas, it is necessary for the incremental costsof power at the boundary of interconnected areas to be the same when itis calculated from either of the interconnected areas. In general anarea's incremental cost at the boundary will increase with increasedpower flow out of the area because of the necessity for increasing itstotal generation. For the purposes of the computations described herein,the functional relationship between the incremental cost and the tieline power flow can be considered monotonic though it need notnecessarily be considered linear. it will be evident that optimumoperation of the power pool 10 of FIG. 1 can be defined as thatoperation which causes an interchange over the tie lines within the poolas well as over the tie lines to external pools as necessary to producethe greatest monetary benefits for the areas of the pool, that is, areas1-4.

For the purpose of computing in each of the areas the desired generationfor each of the generators in the area and the desired power interchangeover the ties to the area, it is advantageous to make the computationsin the area by treating each of the tie lines to the area in a mannerequivalent to the treatment given to a generator in the area. Thus, if aparticular area views an interconnecting tie line it has with anotherarea as being equivalent to a generator in its area whose cost functionis determined by the interconnected area, then the desired power flow onthe interconnecting tie line can be computed by comparing theincremental cost of power at the tie point with the cost of othersources of energy, that is the generators in its own area as well aswith the cost at other tie points. Thus, for each area, optimumoperation within an area is achieved when all sources are supplyingpower at the same values of incremental cost of delivered power, thatis, the cost of power at the hypothetical load center of the area.

For the purpose of computing in each of the computers 31-34 of FIG. 1the desired generation of each of the generators of the separate areasas well as the desired net interchange on the tie lines of the areas,the computers may advantageously be programmed so as to carry out thesteps of computation set forth in FIGS. 2, 3 and 4, which will now beexplained in detail.

In FIG. 2 the economic dispatch computation program is enteredperiodically, for example, every 5 minutes as indicated by block 60. Thefirst block following the block 60 in the flow chart of FIG. 2 is block62 which indicates that the iteration carried on by the program throughthe outer loop of the flow diagram is to be carried on N" times in orderto converge to a solution. As indicated by block 64, the computation ofthe incremental transmission losses associated with power from each ofthe generators of the area as well as the tie lines of the area oP a P,is calculated for each of the inputs to the loss matrix. Thiscalculation which is carried out in accordance with the equation shownin block 66 is a well known calculation and is referred to, for example,on page 49 of the above-mentioned Kirchmayer book, Economic Control ofInterconnected Systems" and on page 75 of "Control of Generation andPower Flow on Interconnected Systems," by Nathan Cohn, published by JohnWiley & Sons, Inc. in 1966. In the equation in block 66, B,,,,, is theappropriate transmission loss coefficient while B is the transmissionloss associated with zero power from the source being considered whileP, represents the output of each of the power sources or transmissionlines being considered in computing the transmission losses.

As indicated by the block 68, the computation of block 66 is continuedfor each of the loss matrix inputs and after the transmission lossassociated with each of the inputs is calculated, the program thencontinues to the step indicated in block 70, namely the setting of A, to8 and the setting of All, to 4, A, being the incremental cost of powerdelivered to the hypothetical load center of the area in which thecomputation is being made. The values 8 and 4 for A, and AA,respectively are to be considered as typical and may be altered toextend or contract the range of It, in the solution. For example, if weassume that the particular program being discussed is being carried outby computer 31 of FIG. 1, then A, the incremental cost of deliveredpower for area 1.

Having set the value of A, and AA, the next step in the program is toenter a series of computations which are repeated M" times, as indicatedby the block 72. The value of M is chosen in accordance with the desiredaccuracy of solution and may be typically set to 20. These computationsinclude first a setting equal to zero of the total desired generation ofthe generating sources P as well as a setting to zero of the value of Ptha is the sum of the desired tie line flow over all of the tie linesbetween the areas interconnected to the area for which the computationis being made. These latter settings are indicated in block 74.

Having made the settings indicated in block 74, the program then entersa portion which is repeated for each of the sources of power, where thesources of power include not only the generators but also the interareatie lines. That repetition of the computations for each of the sourcesis indicated by block 76 which is followed by a branching point 78 whichcauses the program to branch to the series of computations indicated inblock 80 if the source of power is a generator or to the series ofcomputations indicated in block 82 if the source of power is aninterarea tie line. Normally, the computations relating to thegenerators as indicated in block 80 will be carried out first. Thesecomputations include first a computation of the incremental cost at thestation or generator bus for the power provided by the generator. Thatcost is indicated as C, and is calculated as a product of A, (theincremental cost of delivered power in the area) and the quantity (lminus the incremental transmission losses) associated with thegeneration of the particular generator involved.

The generation desired for the generator being considered is a functionof the incremental cost of generation at the generator bus, and for aparticular incremental cost as calculated by the previous calculationthere will be then an associated generation value P, representing theamount of generation required to provide power at the cost figure C, Thenext step in the computation is to compare the level of generationassociated with the computed cost figure C, with the generator's highand low limits, that is, determine whether P, is greater than or equalto the low limit P, or less than or equal to the high limit P,,,. If P,is beyond one of the limits, then the desired generation P will be setto equal either P or P,,,, depending upon which limit is exceeded;otherwise, the desired generation P will be set to equal P, which waspreviously computed as the function of the incremental cost C. The valueP for a particular generator is then added to the total of the values 2Pwhich have been accumulated as a result of the s me computations forother generators and the new total, P,,,, as a result of thiscomputation will then be avai able for summing with the desiredgeneration calculated for the next generator to be considered. The laststep of the computation as shown in block 80 is to store (save) thevalue P for the particular generator being considered as well as the sumof the desired generations.

Following the computations set forth in block 80, the program thencontinues as indicated by block 84 until the computations have been donefor each source of power, as indicated by block 76. If we assume thatall of the generators have been considered and the calculations of thedesired generation for each of them has been determined, then the block78 will cause the computations in block 82 to be made for each of theinterarea tie lines.

The computations for the interarea tie lines include first a computationof the incremental cost at the tie point C, which is calculated in asimilar fashion to the calculation for the costs at the generator busexcept that the incremental loss quantity is computed with regard to thetie line being considered. After the cost C, is computed, it is thennecessary to determine the power flow P, over the tie line which willprovide the level of power flow associated with the calculated cost C Inorder to make this calculation, it is necessary to utilize infonnationtransmitted from the area at the other end of the particular tie linebeing considered; thus, as shown by the second equation in block 82, thevalue of P, is determined by adding to the negative of the tie line flowvalue P transmitted from the foreign area to which the tie interconnectsa quantity which is computed by dividing the difference between the costat the tie point C, and that which was computed in the foreign area CI]! by the rate of change of the tie line cost in the foreign area,namely DCJ OP,],.

The value of P, is then compared as is done in block 80 with the lowerand higher limits set for the tie line, namely P and P,,,, and thedesired tie line power flow P is then set equal to P, if P, is withinthe limits; otherwise it is set equal to the particular limit which isexceeded.

Thus, P the desired power transfer over the tie line being considered,is determined and stored and that value is added to the previouslyaccumulated total P,,, for the tie lines previously considered to get anew tal P which is also then stored for purposes of the next computationrelating to the tie line power flow.

Once all of the generators and all of the interarea tie lines have beenconsidered and the associated desired values for the generation of thegenerators and the power flow over the tie lines has been calculated,the computations carried out by blocks 80 and 82 are not continued andthe comparison shown in block 86 is made. There the absolute value ofthe sum of all of the calculated values for the desired generation ofthe separate generators in the area and the sum of the desired values ofall of the interarea tie lines to the area are compared with themeasured total actual generation of the generators of the area and themeasured total of the tie line power flows between the areas, and if thecomparison gives a value which is not less than a small numbers which isestablished as a criteria for the accuracy to which the iteration is tobe carried, then the program begins a series of steps which are intendedto alter the value of A, either in an upper or a lower directiondepending upon the direction necessary for convergence of the solution.The next step after that shown in block 86 would be the step shown inblock 88 which is carried on as long as the program has not iteratedmore than M times, as shown by block 72, or in other words as long asthe block 89 indicates that the program should continue to iterate thevalue of A The consideration indicated by the steps shown in block 88 iswhether the sum of the total desired generation of the generators in thearea and the total desired power flow over the interarea tie lines isgreater than the actual generation in the area and the actual power flowover the interarea tie lines. if the desired values are greater than theactual values, then, as shown in block 90, A, is decreased by a value AAThe value of AA as computed in block 90 for the next iteration, iscomputed as one half of the present AA whose value may initially be 4,as indicated by block 70. A, may start at a value of 8 as indicated byblock 70. The program then progresses from block to block 72 and anotheriteration is carried out. If the total desired values for the generationand the interarea tie line flows are not greater than the actual values,then the value for A, is increased by a value AA AA, is altered as inblock 90, and the program progresses to block 72 and is continued untilthe computation converges sufficiently or has been carried out M" timesas indicated by block 72.

Should the necessary convergence as tested in block 86 fail tomaterialize within the M" times that the iteration is carried out, thenblock 89 will cause the program to transfer to block 94 which will exitfrom the program and indicate an error. Upon the occurrence of an error,A, will have reached either the upper or the lower value of its range.For the initial value shown in block 70 the range of A, would be zero tosixteen dollars per megawatt hour. An error with a correspondingly highvalue of A, would be an indication of either too little generatingcapacity and/or too little tie line capacity.

When the comparison made in block 86 shows that the iteration of A, iscompleted within the desired accuracy, then the program continues N"times to convergence utilizing for the computation in block 66 the newvalues computed for the various sources, that is the generators andinterarea tie lines as values for P,,,. Actual interarea tie line valuesP could also be used for P,,,, the choice depending on the convergencecharacteristics of a particular power system. Once convergence has beenreached, the next step will be that shown in block 98, namely asummation of the total desired interchange over the interarea ties 2Pwith the actual measured interchange over the ties from the area underconsideration to external pools, namely P so as to thereby obtain thetotal net interchange or the area E P Having obtained the total netinterchange for the area the next series of steps in the program asshown by FIG. 3 is for the purpose of determining the information to besent to the interconnected areas relating to the cost of power at thetie points and the rate of change of that cost with changes in tie linepower flow. The first step in that determination is the step shown inblock where a new value A, is found by summing the A, previously storedwith the value AA After that step, the program goes through the seriesof calculations now to be described for each of the tie lines 1 betweenthe area in which this computer is operating and the other areas withinthe pool which are interconnected to it.

A series of computations is carried out as shown in block 102. The firstcalculation involves the computation of a tie point cost which is to betransmitted from the local area to the interconnected area to which thetie connects C,],. That cost is obtained by computing the product ofA,,, as obtained in block 100, times the quantity (1 minus thetransmission losses over the tie line).

Knowing the cost just calculated, it is possible to compute a fictitiousvalue for the power flow over the tie P" by adding the value P,];, thatis the value received from the interconnected area to the quantityobtained by dividing the difference between the local cost C and thecost at the same tie point r]; 88 sent from the other area by the changein cost with respect to the change in tie line flow as determined andsent from the other area, namely 6G,] an], which represents the slope ofthe cost curve at the interconnected area.

The value P, is then compared with the low limit P and the high limit Pand if the value P, is not beyond either of the limits, then the value Pwhich represents a fictitious desired tie line power flow will be setequal to P,'; whereas if P, exceeds one of the limits, P will be set tothat limit.

Having a fictitious value P determined by changing the value of A by A)it is then possible to determine a AP by subtracting from the fictitiousvalue P the computed desired tie line flow P and checking to see if thatdifference is equal to zero, as shown in block 104. If it is not, thecomputation shown in block 106 is carried out. In block 106 thecomputation involves a determination of the change in cost at the tiepoints with changes in tie power flow as determined from the area atwhich the computer is located, namely OCJ O P,], by multiplying thequantity (1 minus the incremental transmission loss) by the quantity AAand dividing by AP and then subtracting 2 times the constant B (whichrepresents the self constant of the tie as it relates to tie linelosses) and also multiplying by M.

if the quantity AP is equal to zero and thus the statement in block 104is true, then the incremental cost change calculated for the local area,as shown in block 108, is set at a maximum value K and the programproceeds to block 110 where the value for the tie line power flowcalculated at the local area P,], is set equal to P and as indicated bythe block 112, the computation is then repeated for another tie line.

Once the computation in block 106 is made, the next step after thatcomputation is to detennine whether or not the calculated incrementalcost at the tie point, as computed in block 106, was equal or lessthanzero, as shown in block 109. If the value was less than or equal tozero, then the incremental cost in the local area would be set to aminimum value of K as shown in block 111 and the program would progressinto block 110; whereas if the value of the incremental tie point costwas not equal to or less than zero, the program immediately progressesto block 110 and the value of the incremental tie costs for the localarea as computed in block 106 is stored as the incremental cost to besent to the interconnected area along with the sending of the value Pd,and the value C,],.

From the above description of FIG. 3 it will be evident that byincrementing the value of A, the program has computed a cost figure Cd,representing the cost of the power provided by this area to the tiepoint when the power flow is at a value Pd, and a comparable incrementalchange in tie cost 6G,] DE], is also transmitted so that those threeitems of informationcan be utilized in the interconnected area as abasis for determining the amount of power flow which is desired over thetie line for economic operation.

The above discussion of FIGS. 2 and 3 relates specifically to thecomputations which would be carried on in the computers in areas 1, 2and 3 of FIG. 1. Similar computations would be carried on in computer 34of area 4 with the exception of a few minor changes which will now bediscussed. Since area 4 is acting as the reference area, it is necessaryto take into account in determining the incremental cost the magnitudeof the interchange between the reference area and the power pool and theexternal power pool to which it may be connected as by the tie line 23.This change will be evident from the modifications of the algorithmshown in FIG. 2 which should be made as indicated in FIG. 4 for thecomputer 34 of area 4. In FIG. 4 the blocks 98a, 86a and 88a indicatethat those portions of the algorithm have been changed, the block 98abeing utilized in place of the block 98 of FIG. 2 while the blocks 86aand 88a, respectively, replace blocks 86 and 88 of FIG. 2. It will benoted that the block 98a is placed in a different part of the flow chartas compared with the block 98 of FIG. 2 for it is advantageous to makethe calculation set forth in block 980 prior to the entry of theiterative portions of the program where the value calculated in block98a is utilized as, for example, in block 860 and 880.

In block 98:: the desired net interchange of area 4, that is the netinterchange over the interconnecting tie lines 14, I6, 17 and 23, X P iscomputed as the value P representing the actual total net interchangebetween pool 10 and the external pools as measured over theinterconnections 20, 21, 22 and 23 minus the quantity ZQ P whichrepresents the sum of the desired interchange values computed in theforeign areas, that is, the areas interconnected to area 4 andtransmitted to area 4 for this computation over additional communicationchannels not shown in FIG. 1.

Between block 980 and block 86a, the steps of the computation necessaryin area 4 are the same as those previously described for the otherareas.

In area 4, the determination as to whether or not the incremental costiteration has been completed is based upon the absolute value of thedesired generation of area 4 plus the desired net interchange of area 4minus the actual generation of area 4 and also minus the actual netinterchange of area 4. As shown in block 86a, that absolute value iscompared with e and if it is not less than e, the iteration of A,continues as stated in block 89 and the test shown in block 88a is made.

In block 88a the test comprises the comparison of a quantity which is asum of the desired generation as computed for area 4 and the desired tieline interchange as computed for area 4 with the respective actualvalues for those quantities. The program then proceeds in a similarfashion as described with regard to FIG. 2.

The above discussion of FIG. 4 relates specifically to the computationswhich would be carried on in the computers in area 4 of FIG. 1.Different computations could be carried on in the computer 34 of area 4when it is desirable to eliminate the need for additional communicationchannels by making the minor changes which will now be discussed. Thecalculations shown in blocks 86 and 88 would be varied from those shownin FIG. 2 and instead would be as shown in FIG. 5, wherein the block 86band the block 88b respectively replace the blocks 86 and 88 of FIG. 2.As shown in block 8612, the test made involves the comparison of the sumof the desired generations as calculated, namely ZP with the sum of themeasured generations of the area generators P If the absolute value ofthe difference is less than c, then the next step in the computationwould be carried out by block 96 as indicated in FIG. 2; whereasotherwise the next step would be carried out by block 89 which continuesthe computation by carrying out the comparison shown in block 8812 wherethe value P is compared to the value P to see if it is greater than thatvalue. In accordance with the results of that comparison the value A, iseither increased or decreased as previously explained and as set forthin blocks 90 and 91 of FIG. 2.

Under some conditions it is advantageous to utilize in the pool acomputer, at one area only, which acts as a master computer and whichreceives information from each of the areas of the pool indicative ofthe actual generation of each of the generators in those areas as wellas the tie line flows. With that information this master computer cancompute the desired generation values for each of the generators of theseparate areas as well as the desired flow over the individual tie linesand that information can be transmitted to the respective areas as wellas being utilized in the master computer. Basically, this arrangementallows for the use of one master computer without the necessity of usinga loss matrix for all of the tie lines in the pool. it will be evidentto those skilled in the art that either of the systems described indetail, namely for each of the areas with their own computer or withsystems described with a master computer or satellite computer at theother areas, could be used depending upon which would be mostadvantageous for the particular pool involved.

in conjunction with the computations set forth above, each of the areasdesirably incorporates a load frequency control system which willeffectively modify the generation of the generators in the area inaccordance with the computed desired values. The load frequency controlsystem may be operated as a permissive control system utilizing thecomputed (desired) net interchange of the area as a basis fordetennining whether the determination should be increased or decreased.For example, the desired net interchange for the area can be comparedwith the actual net interchange for the area and the difference can bemodified by the existing frequency deviation in the area so as toproduce an area control error sometimes known as area requirement whichcan be utilized as an input to a master controller. The mastercontroller can then produce signals such as pulses of durationcorresponding to the magnitude of the error and those pulses can beselectively allowed to modify the setting of the governor motor of thegenerators in the area in accordance with the relative value of thecomputed value of the desired generation P for a particular generator ascompared with the actual generation 1" of that generator. Such systemsare well known and are illustrated in the above mentioned book by NathanCohn entitled, Control of Generation and Power Flow in interconnectedSystems". Particular reference is directed to that portion of the bookfollowing page 103 dealing with Control Executions. P for example, maybe used as the base point setting for a generator. Participationsettings, which are usually used in conjunction with base points, can bedetermined on the basis of the units regulating capability andassociated economic factors depending upon the nature of the controlsystem desired.

The combination of the computations described by FIGS. 2, 3, 4 and 5 andthe simultaneous control of the generators in the several areas isimportant in that a number of the computations involve the use of actualmeasured values and when the above mentioned computing procedure iscombined with an effective control system operable to carry out thedesired economic distribution, the computation will be effective toprovide accurate values for the desired generation of each of thegenerators and the desired net interchange for the areas.

What is claimed is: l. A method of operating a computing system tocompute the economic distribution of the load among the power sources ineach of a group of areas interconnected for transmission of powertherebetween when at least two of the areas are interconnected by aplurality of transmission lines, comprising the steps of automaticallycomputing a first incremental cost of power at a boundary point on eachtie line between each area and the areas interconnected thereto, saidcomputation being based on the incremental costs and the incrementaltransmission losses in that area, automatically computing in each of theareas interconnected thereto, a second incremental cost of power at thesame boundary points based on the incremental costs and the incrementaltransmission losses in the interconnected areas,

automatically comparing for each area the first and second incrementalcosts calculated for each of the boundary points, and

automatically computing in accordance with the results of saidcomparisons the magnitude of power generation required from each of thepower sources and the net interarea tie line interchange for therespective areas to obtain equality between the sum of the combinationof the total actual generation and interarea tie line interchange andthe combination of the total desired generation and the desired computedinterarea tie line interchange.

2. The method of claim 1 in which the computing system includes acomputer for each of the areas to make the automatic computations forthe areas.

3. The method of claim 1 in which the computing system carries out allof the automatic computations in a single computer.

4. The method of claim 2 in which the computer in each particular areasends to the computers of each of the areas to which it isinterconnected a signal representative of the incremental cost of powerat the boundary point of each of the individual tie lines to thoseinterconnected areas for the existing level of incremental cost ofdelivered power for the area.

5. The method of claim 4 in which the computer in each particular areasends to the computer of each of the areas to which it is interconnecteda signal representative of the level of power flow associated with theincremental cost sent to the interconnected areas and signalsrepresentative of the rate of change of the incremental cost at each ofthe tie points associated with said level of tie line power flow.

6. A method of operating a computing system to compute the economicdistribution of the load among the power sources in each of a group ofareas intercom nected for transmission of power therebetween when atleast two of the areas are interconnected by a plurality of transmissionlines, comprising the steps of automatically computing a firstincremental cost of power at a boundary point on each tie line betweeneach area and the areas interconnected thereto, said computation beingbased on the incremental costs and the incremental transmission lossesin the area involved in computation, automatically computing in each ofthe areas interconnected thereto, a second incremental cost of power atthe same boundary points based on the incremental costs and theincremental transmission losses in the interconnected areas,automatically comparing for each area the first and second incrementalcosts calculated for each of the boundary points,

automatically computing from the results of said comparison themagnitude of power interchange required on each of the tie lines toobtain an economic interchange of power,

automatically computing in each area an incremental cost for generatingpower from each source of the area,

automatically computing in accordance with said last-named costs theassociated desired generation for each of the sources,

comparing the sum of the combined total generation and total desired tieline flow for the area with the combination of the total actualgeneration and the total actual tie line flow for the area, and

adjusting the incremental cost of delivered power for the area to bringsaid sum towards zero.

1. A method of operating a computing system to compute the economicdistribution of the load among the power sources in each of a group ofareas interconnected for transmission of power therebetween when atleast two of the areas are interconnected by a plurality of transmissionlines, comprising the steps of automatically computing a firstincremental cost of power at a boundary point on each tie line betweeneach area and the areas interconnected thereto, said computation beingbased on the incremental costs and the incremental transmission lossesin that area, automatically computing in each of the areasinterconnected thereto, a second incremental cost of power at the sameboundary points based on the incremental costs and the incrementaltransmission losses in the interconnected areas, automatically comparingfor each area the first and second incremental costs calculated for eachof the boundary points, and automatically computing in accordance withthe results of said comparisons the magnitude of power generationrequired from each of the power sources and the net interarea tie lineinterchange for the respective areas to obtain equality between the sumof the combination of the total actual generation and interarea tie lineinterchange and the combination of the total desired generation and thedesired computed interarea tie line interchange.
 2. The method of claim1 in which the computing system includes a computer for each of theareas to make the automatic computations for the areas.
 3. The method ofclaim 1 in which the computing system carries out all of the automaticcomputations in a single computer.
 4. The method of claim 2 in which thecomputer in each particular area sends to the computers of each of theareas to which it is interconnected a signal representative of theincremental cost of power at the boundary point of each of theindividual tie lines to those interconnected areas for the existinglevel of incremental cost of delivered power for the area.
 5. The methodof claim 4 in which the computer in each particular area sends to thecomputer of each of the areas to which it is interconnected a signalrepresentative of the level of power flow associated with theincremental cost sent to the interconnected areas and signalsrepresentative of the rate of change of the incremental cost at each ofthe tie points associated with said level of tie line power flow.
 6. Amethod of operating a computing system to compute the economicdistribution of the load among the power sources in each of a group ofareas interconnected for transmission of power therebetween when atleast two of the areas are interconnected by a plurality of transmissionlines, comprising the steps of automatically computing a firstincremental cost of power at a boundary point on each tie line betweeneach area and the areas interconnected thereto, said computation beinGbased on the incremental costs and the incremental transmission lossesin the area involved in computation, automatically computing in each ofthe areas interconnected thereto, a second incremental cost of power atthe same boundary points based on the incremental costs and theincremental transmission losses in the interconnected areas,automatically comparing for each area the first and second incrementalcosts calculated for each of the boundary points, automaticallycomputing from the results of said comparison the magnitude of powerinterchange required on each of the tie lines to obtain an economicinterchange of power, automatically computing in each area anincremental cost for generating power from each source of the area,automatically computing in accordance with said last-named costs theassociated desired generation for each of the sources, comparing the sumof the combined total generation and total desired tie line flow for thearea with the combination of the total actual generation and the totalactual tie line flow for the area, and adjusting the incremental cost ofdelivered power for the area to bring said sum towards zero.